Respuesta :
Polynomial is an expression that consists of indeterminates(variable) and coefficient. The polynomial f(x) is x³-12x²+256=0.
What are polynomial?
Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
As the zeros of the polynomial are 8(multiplicity 2), -4. Therefore, the factors of the polynomial can be written as,
[tex]x = 8\\x-8=0[/tex]
[tex]x =-4\\x+4=0[/tex]
Now, the polynomial f(x) which is a third-degree polynomial can be written as,
[tex](x-8)(x-8)(x+4)=0\\\\(x-8)^2(x+4)=0\\\\(x^2-16x+64)(x+4)=0\\\\x^3-16x^2+64x+4x^2-64x+256 = 0\\\\x^3-12x^2+256=0[/tex]
Hence, the polynomial f(x) is x³-12x²+256=0.
Learn more about Polynomial:
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